Computing correct confidence intervals for ANOVA fixed- And random-effects effect sizes

Abstract

Most textbooks explain how to compute confidence intervals for means, correlation coefficients, and other statistics using "central" west distributions (e.g., t, F) that are appropriate for such statistics. However, few textbooks explain how to use "noncentral" test distributions (e.g., noncentral t, noncentral F) to evaluate power or to compute confidence intervals for effect sizes. This article illustrates the computation of confidence intervals for effect sizes for some ANOVA applications; the use of intervals invoking noncentral distributions is made practical by newer software. Greater emphasis on both effect sizes and confidence intervals was recommended by the APA Task Force on Statis..